Lexicographic pseudo MV-algebras

A lexicographic pseudo MV-algebra is an algebra that is isomorphic to an interval in the lexicographic product of a unital linearly ordered group with an arbitrary e-group. We present conditions when a pseudo MV-algebra is lexicographic. We show that a key condition is the existence of a lexicographic ideal, or equivalently, a case when the algebra can be split into comparable slices indexed by elements of the interval [0,u] of some unital linearly ordered group (H, u). Finally, we show that fixing (H, u), the category of (H, u)-lexicographic pseudo MV-algebras is categorically equivalent to the category of R-groups. (C) 2015 Elsevier B.V. All rights reserved.